Dallas was born in Philadelphia, Pennsylvania, and graduated from the College of New Jersey (now Princeton University) in 1810. He was admitted to the bar in 1813, and served as private secretary to Albert Gallatin, Minister to Russia. Dallas returned in 1814 and practiced law in New York City. He was solicitor of the United States Bank from 1815 to 1817. He returned to Philadelphia and was appointed deputy attorney general in 1817. He was mayor of Philadelphia from October 21, 1828 to April 15, 1829. Dallas was United States district attorney for the eastern district of Pennsylvania from 1829 to 1831. He was elected as a Democrat to the United States Senate to fill the vacancy caused by the resignation of Isaac D. Barnard and served from December 13, 1831 to March 3, 1833, when he declined to be a candidate for reelection. He was chairman of the Committee on Naval Affairs.
Dallas resumed the practice of law. He was attorney general of Pennsylvania from 1833 to 1835. He was appointed by President Martin Van Buren as Envoy Extraordinary and Minister Plenipotentiary to Russia from 1837 to 1839, when he was recalled at his own request. He was elected Vice President of the United States on the Democratic ticket in 1844 with James K. Polk and served from March 4, 1845 to March 3, 1849.
Dallas was appointed Envoy Extraordinary and Minister Plenipotentiary to Great Britain by President Franklin Pierce from 1856 to 1861, when he returned to Philadelphia, and died there. He is interred in St. Peterís Churchyard. The city of Dallas, Texas and others are named in his honor.